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Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

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The asymptotic convexity of the negative likelihood function of GARCH models

Ip, W. and Wong, H. and Pan, J. and Li, D.F. (2006) The asymptotic convexity of the negative likelihood function of GARCH models. Computational Statistics and Data Analysis, 50 (2). pp. 311-331. ISSN 0167-9473

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Abstract

We prove the convexity of the negative likelihood function in the asymptotic sense for GARCH models. This property provides assurance for the convergence of numerical optimization algorithms for maximum likelihood estimation of GARCH. A simulation study is conducted in order to compare the performance of several different iteration algorithms. An example based on the log-returns of foreign exchange rates is also given.